Density of strings formed at a second-order cosmological phase transition

We discuss the problem of estimating the characteristic length scale ${\xi }_{\mathrm{s}}$, and hence the initial density, of a system of cosmic strings formed at a continuous, second-order phase transition in the early universe. In particular, we examine the roles of the correlation length (or string width) ${\xi }_{\mathrm{c}}$ and the Ginzburg length ${\xi }_{\mathrm{G}}$ which defines the ``fuzziness’’ of long strings. We argue that strings acquire a clear identity only once ${\xi }_{\mathrm{s}}$ exceeds both ${\xi }_{\mathrm{c}}$ and ${\xi }_{\mathrm{G}}$, and estimate its magnitude at that time.